U.S. patent application number 11/239135 was filed with the patent office on 2006-03-30 for capture and display of image of three-dimensional object.
Invention is credited to Daniel Benzano.
Application Number | 20060066877 11/239135 |
Document ID | / |
Family ID | 36098685 |
Filed Date | 2006-03-30 |
United States Patent
Application |
20060066877 |
Kind Code |
A1 |
Benzano; Daniel |
March 30, 2006 |
Capture and display of image of three-dimensional object
Abstract
A system and method for modeling three-dimensional objects such
as diamonds and other gemstones. A three-dimensional finite-element
model obtained by, for example, analysis of boundaries of the
object in photographs taken from multiple perspectives with frontal
lighting or silhouette lighting, or by analysis of structured-light
photographs of the object taken from multiple perspectives, is
combined with color or grayscale information obtained from
photographs of the object. Enhanced or "false" color can be used to
improve the viewing experience or to emphasize particular features
of the object. A computer can rotate the model about arbitrary axes
according to the desires of a viewer.
Inventors: |
Benzano; Daniel; (Ramat Gan,
IL) |
Correspondence
Address: |
DR. MARK FRIEDMAN LTD.;C/o Bill Polkinghorn
9003 Florin Way
Upper Marlboro
MD
20772
US
|
Family ID: |
36098685 |
Appl. No.: |
11/239135 |
Filed: |
September 30, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60614048 |
Sep 30, 2004 |
|
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Current U.S.
Class: |
356/603 |
Current CPC
Class: |
G06T 1/0007 20130101;
G01N 21/87 20130101; G01B 11/25 20130101 |
Class at
Publication: |
356/603 |
International
Class: |
G01B 11/24 20060101
G01B011/24 |
Foreign Application Data
Date |
Code |
Application Number |
Jan 30, 2005 |
IL |
166574 |
Claims
1. A modeling system comprising: (a) a modeling mechanism operative
to create a geometric model of at least a portion of an object; (b)
an imaging mechanism operative to obtain at least one reflectivity
image of said object, and (c) a mapping mechanism operative to map
at least a portion of a said reflectivity image to at least a
portion of said geometric model so as to provide a reflectivity
model of at least a portion of said object.
2. The system of claim 1, wherein said imaging mechanism is
operative to obtain a plurality of said images taken from a
plurality of perspectives.
3. The system of claim 2, wherein said perspectives include angles
disposed about an axis.
4. The system of claim 3, further comprising: (d) a holder
operative to hold and rotate said object, and wherein said
perspectives are obtained by rotation of said object by said
holder.
5. The system of claim 4, wherein said holder includes a vacuum
mechanism operative to secure said object to said holder.
6. The system of claim 1, wherein said object includes a diffusing
coating.
7. The system of claim 1, wherein said object includes at least one
mark.
8. The system of claim 1, wherein said object includes a
gemstone.
9. The system of claim 1, wherein said object includes a component
selected from the group consisting of a diamond, an emerald and a
ruby.
10. The system of claim 1, further comprising: (d) an enclosure
operative to isolate at least one component of the modeling system,
selected from the group consisting of said modeling mechanism and
said imaging mechanism, from stray light.
11. The system of claim 1, wherein said modeling mechanism includes
a camera.
12. The system of claim 11, wherein said camera includes a digital
camera.
13. The system of claim 1, wherein said modeling mechanism includes
a source of structured light.
14. The system of claim 13, wherein said source of structured light
is operative to produce a beam having a substantially linear
cross-section.
15. The system of claim 13, wherein said source of structured light
includes a laser.
16. The system of claim 1, wherein said modeling mechanism is
operative to create said geometric model from a plurality of
boundaries of said object, said boundaries being obtained from a
plurality of images of said object.
17. The system of claim 16, wherein at least one said image from
which a corresponding said boundary is obtained is a silhouette
image of said object.
18. The system of claim 16, wherein at least one said image from
which a corresponding said boundary is obtained is a reflectivity
image of said object.
19. The system of claim 1, wherein said imaging mechanism includes
a camera.
20. The system of claim 19, wherein said camera includes a digital
camera.
21. The system of claim 1, wherein said imaging system includes a
light source.
22. The system of claim 21, wherein said light source includes a
light-emitting element selected from the group consisting of a
light-emitting diode, a discharge lamp, a fluorescent lamp, an
electroluminescent light, a laser and an incandescent lamp.
23. The system of claim 1, wherein said geometric model includes
information from a structured-light image and information from an
image selected from the group consisting of a reflectivity image
and a silhouette image.
24. The system of claim 1, wherein said geometric model includes a
three-dimensional finite-element model.
25. The system of claim 1, further comprising: (d) a display device
operative to show reflectivity of at least a portion of a surface
of said object.
26. The system of claim 1, wherein said reflectivity model includes
reflectivity information selected from the group consisting of
grayscale information, color information, and enhanced color
information.
27. The system of claim 1, wherein the modeling system is operative
to rotate said reflectivity model through an arbitrary angle about
an arbitrary axis.
28. A modeling method comprising the steps of: (a) obtaining a
geometric model of at least a portion of a surface of an object;
(b) obtaining at least one reflectivity image of said object, and
(c) combining said geometric model and reflectivity data from said
reflectivity image to obtain a reflectivity model of at least a
portion of said object.
29. The method of claim 28, wherein a plurality of said
reflectivity images is obtained from a plurality of
perspectives.
30. The method of claim 29, further comprising the step of: (d)
rotating said object to obtain said plurality of perspectives.
31. The method of claim 28, further comprising the step of: (d)
applying a diffusing coating to said object.
32. The method of claim 28, further comprising the step of: (d)
marking said object.
33. The method of claim 28, wherein said object includes a
gemstone.
34. The method of claim 28, wherein said object includes a
component selected from the group consisting of a diamond, an
emerald and a ruby.
35. The method of claim 28, wherein said modeling is effected by
steps including illuminating said object with structured light.
36. The method of claim 35, wherein said structured light includes
a beam having a substantially linear cross-section.
37. The method of claim 28, wherein said obtaining of said
geometric model includes: (i) obtaining images of said object from
at least two perspectives; (ii) extracting boundaries from said
images, and (iii) creating said geometric model from said
boundaries.
38. The method of claim 37, wherein at least one said image is a
silhouette image of said object.
39. The method of claim 37, wherein at least one said image is a
reflectivity image of said object.
40. The method of claim 28, further comprising the step of: (d)
illuminating said object with a light source selected from the
group consisting of a light emitting diode, a discharge lamp, a
fluorescent lamp, an electroluminescent light, a laser and an
incandescent lamp.
41. The method of claim 28, wherein said obtaining of said
geometric model includes obtaining at least one structured-light
image of said object and at least one image, of said object,
selected from the group consisting of a reflectivity image and a
silhouette image, said geometric model being based on said
images.
42. The method of claim 28, wherein said geometric model includes a
three-dimensional finite-element model.
43. The method of claim 28, further comprising the step of: (d)
displaying reflectivity of at least a portion of a surface of said
object.
44. The method of claim 28, wherein said reflectivity model
includes reflectivity information selected from the group
consisting of grayscale information, color information, and
enhanced color information.
45. The method of claim 28, further comprising the step of: (d)
rotating said reflectivity model through an arbitrary angle about
an arbitrary axis.
46. A machine readable storage medium having stored thereon machine
executable instructions, the execution of said machine executable
instructions implementing a method for modeling, the method
comprising the steps of: (a) obtaining a geometric model of at
least a portion of a surface of an object; (b) obtaining at least
one reflectivity image of said object, and (c) combining said
geometric model and reflectivity data from said reflectivity image
to obtain a reflectivity model of at least a portion of said
object.
47. The machine readable storage medium of claim 46, wherein said
object includes a gemstone.
48. The machine readable storage medium of claim 46, wherein said
object includes a component selected from the group consisting of a
diamond, an emerald and a ruby.
Description
[0001] This is a continuation-in-part of U.S. Provisional Patent
Application No. 60/614,048, filed Sep. 30, 2004 and claims priority
of Israel Patent Application No. 166574 filed Jan. 30, 2005.
FIELD AND BACKGROUND OF THE INVENTION
[0002] The present invention relates to a system and method for
capturing and displaying an image of a three-dimensional object,
and, more particularly, to a system and method wherein a
three-dimensional finite-element model of the outer surface of the
object is combined with photographs of the object taken from
multiple angles and displayed on a display device such as a
computer screen. The photographic data are used to assign color or
grayscale values to the elements of the three-dimensional model.
The object is then displayed using a combination of the information
from the three-dimensional model and the color or grayscale values,
providing a realistic view of the object, including any surface
markings. The three-dimensional model can be rotated about any axis
to provide the user with an experience very similar to examining
the object while holding the object in one's hands.
[0003] Such a system is particularly desirable for the display of
uncut, or rough, precious stones, where it is desirable to
determine whether a particular rough stone can be cut to a
particular shape.
[0004] Such a system is also desirable for such activities as
virtually displaying a precious stone to a potential purchaser, in
that realistic display of the stone is provided without the risks,
such as loss or theft, involved in transporting and displaying a
precious stone.
[0005] Rough precious stones are often marked with markings that
serve as aids and guides to help both in deciding how the stone is
to be cut, and in the actual cutting and shaping of the stone. The
system of the present invention allows such markings to be seen as
part of the virtual image of the stone, which is highly
advantageous in the analysis of the stone, and in presenting and
explaining possible final shapes for the stone, especially to
persons with limited expertise in the field of precious stones.
[0006] Various attempts have been made to capture and display
images of three-dimensional objects such as precious stones. U.S.
Pat. No. 6,567,156 describes the combination of silhouette images
and structured light triangulation to produce a three-dimensional
map of the surface of an object, including recesses on the surface
of the object. However, the map provided according to U.S. Pat. No.
6,567,156 does not provide information to a viewer regarding the
color or reflectivity of the surface of the object, nor is there a
provision for viewing of the mapped object from arbitrary
angles.
[0007] There is thus a widely recognized need for, and it would be
highly advantageous to have, a system and method for capturing a
three-dimensional image of the surface of an object, such as a
precious stone, including the reflectivity and/or color of the
surface of the object, and displaying the three-dimensional image
as a grayscale or color image that can be rotated by the viewer
about arbitrary axes.
SUMMARY OF THE INVENTION
[0008] In a system according to the present invention, a
three-dimensional finite-element model of an object and photographs
of the object are combined into an enhanced three-dimensional
finite-element model that includes color and/or reflectivity
information for the elements of the model. To a viewer, the effect
is as if the photographs had been pasted onto the three-dimensional
finite-element model. Such an enhanced model of the object provides
a very realistic viewing experience.
[0009] According to the present invention there is provided a
modeling system including: (a) a modeling mechanism operative to
create a geometric model of at least a portion of an object; (b) an
imaging mechanism operative to obtain at least one reflectivity
image of the object, and (c) a mapping mechanism operative to map
at least a portion of a the reflectivity image to at least a
portion of the geometric model so as to provide a reflectivity
model of at least a portion of the object.
[0010] Preferably, in the system, the imaging mechanism is
operative to obtain a plurality of images taken from a plurality of
perspectives.
[0011] Preferably, in the system, the perspectives include angles
disposed about an axis.
[0012] Preferably, the system further includes: (d) a holder
operative to hold and rotate the object, and the perspectives are
obtained by rotation of the object by the holder.
[0013] Preferably, in the system, the holder includes a vacuum
mechanism operative to secure the object to the holder.
[0014] Preferably, in the system, the object includes a diffusing
coating.
[0015] Optionally, in the system, the object includes at least one
mark.
[0016] Preferably, in the system, the object includes a
gemstone.
[0017] Preferably, in the system, the object includes a component
selected from the group consisting of a diamond, an emerald and a
ruby.
[0018] Preferably, the system further includes: (d) an enclosure
operative to isolate at least one component of the modeling system,
selected from the group consisting of the modeling mechanism and
the imaging mechanism, from stray light.
[0019] Preferably, in the system, the modeling mechanism includes a
camera.
[0020] Preferably, in the system, the camera includes a digital
camera.
[0021] Preferably, in the system, the modeling mechanism includes a
source of structured light.
[0022] Preferably, in the system, the source of structured light is
operative to produce a beam having a substantially linear
cross-section.
[0023] Preferably, in the system, the source of structured light
includes a laser.
[0024] Alternatively, in the system, the modeling mechanism is
operative to create the geometric model from a plurality of
boundaries of the object, the boundaries being obtained from a
plurality of images of the object.
[0025] Preferably, in the system, at least one image from which a
corresponding boundary is obtained is a silhouette image of the
object.
[0026] Alternatively, in the system, at least one image from which
a corresponding boundary is obtained is a reflectivity image of the
object.
[0027] Preferably, in the system, the imaging mechanism includes a
camera.
[0028] Preferably, in the system the camera includes a digital
camera.
[0029] Preferably, in the system, the imaging system includes a
light source.
[0030] Preferably, in the system, the light source includes a
light-emitting element selected from the group consisting of a
light-emitting diode, a discharge lamp, a fluorescent lamp, an
electroluminescent light, a laser and an incandescent lamp.
[0031] Preferably, in the system, the geometric model includes
information from a structured-light image and information from an
image selected from the group consisting of a reflectivity image
and a silhouette image.
[0032] Preferably, in the system, the geometric model includes a
three-dimensional finite-element model.
[0033] Preferably, the system further includes: (d) a display
device operative to show reflectivity of at least a portion of a
surface of the object.
[0034] Preferably, in the system, the reflectivity model includes
reflectivity information selected from the group consisting of
grayscale information, color information, and enhanced color
information.
[0035] Preferably, in the system, the modeling system is operative
to rotate the reflectivity model through an arbitrary angle about
an arbitrary axis.
[0036] According to the present invention there is provided a
modeling method including the steps of: (a) obtaining a geometric
model of at least a portion of a surface of an object; (b)
obtaining at least one reflectivity image of the object, and (c)
combining the geometric model and reflectivity data from the
reflectivity image to obtain a reflectivity model of at least a
portion of the object.
[0037] Preferably, in the method, a plurality of the reflectivity
images is obtained from a plurality of perspectives.
[0038] Preferably, the method further includes the step of: (d)
rotating the object to obtain the plurality of perspectives.
[0039] Preferably, the method further includes the step of: (d)
applying a diffusing coating to the object.
[0040] Optionally, the method further includes the step of: (d)
marking the object.
[0041] Preferably, in the method, the object includes a
gemstone.
[0042] Preferably, in the method, the object includes a component
selected from the group consisting of a diamond, an emerald and a
ruby.
[0043] Preferably, in the method, the modeling is effected by steps
including illuminating the object with structured light.
[0044] Preferably, in the method, the structured light includes a
beam having a substantially linear cross-section.
[0045] Alternatively, in the method, the obtaining of the geometric
model includes: (i) obtaining images of the object from at least
two perspectives; (ii) extracting boundaries from the images, and
(iii) creating the geometric model from the boundaries.
[0046] Preferably, in the method, at least one image is a
silhouette image of the object.
[0047] Alternatively, in the method, at least one image is a
reflectivity image of the object.
[0048] Preferably, the method further includes the step of: (d)
illuminating the object with a light source selected from the group
consisting of a light emitting diode, a discharge lamp, a
fluorescent lamp, an electroluminescent light, a laser and an
incandescent lamp.
[0049] Preferably, in the method, the obtaining of the geometric
model includes obtaining at least one structured-light image of the
object and at least one image, of the object, selected from the
group consisting of a reflectivity image and a silhouette image,
the geometric model being based on the images.
[0050] Preferably, in the method, the geometric model includes a
three-dimensional finite-element model.
[0051] Preferably, the method further includes the step of: (d)
displaying reflectivity of at least a portion of a surface of the
object.
[0052] Preferably, in the method, the reflectivity model includes
reflectivity information selected from the group consisting of
grayscale information, color information, and enhanced color
information.
[0053] Preferably, the method further includes the step of: (d)
rotating the reflectivity model through an arbitrary angle about an
arbitrary axis.
[0054] According to the present invention there is provided a
machine readable storage medium having stored thereon machine
executable instructions, the execution of the machine executable
instructions implementing a method for modeling, the method
including the steps of: (a) obtaining a geometric model of at least
a portion of a surface of an object; (b) obtaining at least one
reflectivity image of the object, and (c) combining the geometric
model and reflectivity data from the reflectivity image to obtain a
reflectivity model of at least a portion of the object.
[0055] Preferably, in the machine readable storage medium, the
object includes a gemstone.
[0056] Preferably, in the machine readable storage medium, the
object includes a component selected from the group consisting of a
diamond, an emerald and a ruby.
BRIEF DESCRIPTION OF THE DRAWINGS
[0057] The invention is herein described, by way of example only,
with reference to the accompanying drawings, wherein:
[0058] FIG. 1a illustrates schematically a plan view of a system
for image capture according to the present invention;
[0059] FIG. 1b illustrates schematically a plan view of an
alternative system for image capture according to the present
invention, incorporating a source of structured light;
[0060] FIG. 1c illustrates schematically a plan view of an
alternative system for image capture according to the present
invention, incorporating a source of silhouette lighting;
[0061] FIG. 2 illustrates schematically a three-dimensional
coordinate system for an object;
[0062] FIG. 3 illustrates schematically a two-dimensional
coordinate system for a photograph of an object;
[0063] FIG. 4a is a photographic image of an object taken with an
apparatus according to the present invention;
[0064] FIG. 4b is a photographic image of the object depicted in
FIG. 4a, after rotation, taken with an apparatus according to the
present invention;
[0065] FIG. 5a is a photographic image of the object depicted in
FIG. 4a, in the same position as in FIG. 4a, illuminated with a
source of structured light;
[0066] FIG. 5b is a photographic image of the object depicted in
FIG. 4a, in the same position as in FIG. 4b, illuminated with a
source of structured light;
[0067] FIG. 6a is a photographic image of the object depicted in
FIG. 4a, in the same position as in FIG. 4a, illuminated from
behind to produce a silhouette image;
[0068] FIG. 6b is a photographic image of the object depicted in
FIG. 4a, in the same position as in FIG. 4b, illuminated from
behind to produce a silhouette image;
[0069] FIG. 7a illustrates schematically an elevation view of a
system for structured lighting of an object;
[0070] FIG. 7b illustrates schematically a plan view of the system
of FIG. 7a for structured lighting of an object
[0071] FIG. 8a illustrates schematically an elevation view of a
system according to the present invention wherein the optical axis
of the camera is substantially perpendicular to the axis of
rotation of an object;
[0072] FIG. 8b illustrates schematically an elevation view of a
system according to the present invention wherein the optical axis
of the camera forms an acute angle with the axis of rotation of an
object;
[0073] FIG. 9 illustrates schematically a system according to the
present invention including a computer and a storage medium
containing instructions operative to control the operation of the
system.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0074] The present invention is of a system and method which can be
used to capture and display images of a three-dimensional object so
that a user is presented with an image that shows the reflectivity
and/or color of the surface of the object, and so that the user can
select to view the object as if rotated arbitrarily in space.
[0075] The principles and operation of a system for capturing and
displaying images of a three-dimensional object according to the
present invention may be better understood with reference to the
drawings and the accompanying description.
[0076] Referring now to the drawings, FIG. 1a illustrates
schematically a first embodiment of the present invention, in which
an object 16 is held on a rotatable support, or dop, 24.
Optionally, object 16 is coated with a preferably removable coating
that diffuses light. Coating object 16 is particularly advantageous
if object 16 is transparent and/or reflective. Marks can be made on
the coating. If the coating is sufficiently thin and made of
appropriate material, surface marks on object 16 will be visible
through the coating. Preferably, object 16 is held onto dop 24 by a
vacuum mechanism. An enclosure 50 is operative to suppress stray
light.
[0077] Object 16 is illuminated by a lamp 18 and photographed by a
camera 12, and then rotated through an angle by dop 24, the angle
preferably having measure of at least 0.1 degree and no greater
than 20 degrees, and, still more preferably, having measure of at
least 0.5 degree and no greater than 5 degrees, the angle also
preferably having measure substantially equal to a full circle
divided by an integer, before being photographed again. Although
rotation of object 16 through substantially uniform angles meeting
the above criteria between consecutive photographings of object 16
is preferred because it simplifies mathematical manipulation of the
images, the use of non-uniform angles and/or an angle not meeting
the above criteria is within the scope of the present invention.
This procedure is repeated until object 16 has been rotated through
substantially a full rotation, and a set of reflectivity
photographs including information about the reflectivity of the
surface of object 16 as viewed from multiple angles is
obtained.
[0078] Lamp 18 illuminates object 16 frontally, so that
reflectivity photographs produced during the rotation of object 16
include information about the reflectivity and/or color of the
surface regions of object 16. Lamp 18 may include, but is not
limited to, a light-emitting diode, a discharge lamp, a fluorescent
lamp, an electroluminescent light, a laser or an incandescent
lamp.
[0079] Examples of such reflectivity photographs are shown in FIGS.
4a and 4b, wherein object 16 rests upon dop 24, dop 24 being
operative to rotate object 16 about an axis 28. A reflection 26 of
lamp 18 is an artifact of the prototype system used to produce
FIGS. 4a and 4b, and such artifacts can be suppressed by
appropriate design of enclosure 50 and use of low-reflectivity
materials, or image-processing software can effectively eliminate
or compensate for such artifacts.
[0080] Preferably, camera 12 in FIG. 1a is a solid-state camera,
such as a charge-coupled device (CCD) camera, although other types
of cameras may be used, and the use of any type of camera 12 is
within the scope of the present invention. Preferably, camera 12 is
a digital camera connected to a modeling mechanism such as a
computer 10. Computer 10 is not necessarily limited to this role in
the system of the present invention, and can also perform other
functions in the system, as indicated below. Through
image-processing techniques well-known in the art, such as, for
example, threshholding, a boundary of object 16 is determined for
each of the reflectivity photographs. The boundaries thus
determined are then used to create a three-dimensional
finite-element model of the surface of object 16 using techniques
well-known in the art, as used, for example, in the OGI-Rough
System, OGI Systems, Ltd., Ramat Gan, Israel.
[0081] The reflectivity measurements included in the reflectivity
photographs are then mapped onto the three-dimensional model.
Preferably, this mapping is performed by a mapping mechanism, such
as computer 10. This mapping assigns a reflectivity value to each
element of the three-dimensional finite-element model. The
reflectivity information can be monochrome, or can include
information indicating color. The three-dimensional finite-element
model, enhanced with reflectivity information, thus produced
provides the information needed to display, using systems and
methods well-know in the art, as used, for example, in the
aforementioned OGI-Rough System, a realistic image of object 16 on
a display device 32, and this image can rotated by the user about
arbitrary axes. Such systems and methods can provide for grayscale
and/or color display, including, optionally, enhanced, or "false",
color. Preferably, the finite-element three-dimensional model
includes a fine-mesh model of the surface of object 16. The
elements of the three-dimensional model can be of arbitrary shape
and can include triangles and quadrilateral figures. Preferably,
the elements are triangular, although elements of any shape are
within the scope of the present invention. Preferably, the
reflectivity value assigned to any particular triangular element is
an average of the reflectivity values determined for the three
vertices of the triangle. Alternatively, reflectivity values can be
determined by other functions, including, but not limited to, the
reflectivity value of a single, arbitrarily selected point on the
surface of the triangle, or a weighted average of a collection of
points on or near the surface of the triangle. Such alternative
determinations of reflectivity values are included within the scope
of the present invention. Reflectivity values for elements having
other shapes can be determined by similar mechanisms adapted to
those shapes, and such mechanisms are included within the scope of
the present invention.
[0082] FIG. 2 illustrates schematically a coordinate system for
object 16, applicable to this embodiment. The coordinate system of
FIG. 2 is fixed to object 16, and thus rotates along with object 16
as object 16 is rotated. The Z-axis of the coordinate system of
FIG. 2 corresponds to the axis of rotation of dop 24. FIG. 3
illustrates schematically a coordinate system for the P.sup.th
two-dimensional reflectivity photograph of object 16, where P is an
index into a set of N.sub.c two-dimensional reflectivity
photographs of object 16. The N.sub.c photographs are taken with
object 16 rotated through an angle substantially equal to
360.degree./N.sub.c between the taking of successive photographs.
The coordinate system of FIG. 3 remains fixed relative to camera 12
as object 16 is rotated. Taking into account the relative rotation
of the respective coordinate systems of FIG. 2 and FIG. 3, the
mapping from a three-dimensional point (X, Y, Z) on object 16 in
the coordinate system of FIG. 2 to a point (X'.sub.P, Z'.sub.P) on
the P.sup.th two-dimensional reflectivity photograph from a total
of N.sub.c two-dimensional reflectivity photographs is according to
the formulae: X'.sub.P=X cos .alpha.-Y sin .alpha. (1) and
Z'.sub.P=Z (2) where .alpha.=2.pi.P/N.sub.c
[0083] This embodiment has the advantage of requiring only a single
set of photographs to both capture reflectivity information and
produce a three-dimensional finite-element model of object 16. Some
other embodiments, some of which are discussed below, require a
second set of photographs to produce a three-dimensional
finite-element model of object 16. Although determination of
boundaries of object 16 from reflectivity photographs can be
computation-intensive and subject to error, the elimination of the
need for a second set of photographs has several compensatory
advantages. Rotating object 16 takes time. Although it is possible,
if camera 12 is sufficiently fast, for camera 12 to photograph
object 16 while object 16 is rotating, it is preferable, in order
for the photographs to be as clear as possible, for object 16 to be
stopped, relative to camera 12, at the time that object 16 is
photographed by camera 12. The time required to rotate object 16
for a second set of photographs, including the time required for
object 16 to settle at each step of the rotation, can be more than
the extra time required by computer 10 to determine the boundaries
of object 16 from reflectivity photographs relative to the time
required by computer 10 to determine the boundaries of object 16 by
other techniques. Although, in the embodiments discussed below
which require two sets of photographs of object 16, it is possible
to produce both sets with a single rotation of object 16, the two
different types of photographs require different lighting of object
16, as discussed below. This requires changing the lighting of
object 16 at every step of the rotation. Thus, if the light sources
involved require time to stabilize after being turned on, or if the
light sources exhibit afterglow after being turned off, the time
required to photograph object 16 is correspondingly increased, the
increase being proportional to the number of rotational steps.
Being repeatedly turned on and off can cause rapid wear of some
light sources, notably incandescent lamps. This embodiment also
reduces the memory requirement of the system, because only one set
of photographs need be stored.
[0084] Alternatively, only a half-rotation of object 16 is
necessary to provide the information about the boundaries of object
16 necessary to construct a three-dimensional model of object 16.
This is because rotation of object 16 by a half-rotation about axis
28 simply reflects the positions of boundary points of object 16
about axis 28, without providing any new boundary information about
object 16. Thus, if photographs corresponding to a full rotation of
object 16 were to be used for constructing a three-dimensional
model of object 16, a photograph taken during the second
half-rotation of object 16 would include substantially the same
information about the boundaries of object 16 as would be included
in a photograph of object 16 taken a half-rotation earlier during
the first half-rotation of object 16. Therefore, the
three-dimensional model can be determined using reflectivity
photographs corresponding to only a half-rotation of object 16.
However, rotation of object 16 by a half-rotation about axis 28
does present new reflectivity information to camera 12, and it is
thus desirable to make use of reflectivity photographs
corresponding to a substantially full rotation of object 16 about
axis 28.
[0085] A second, alternative, embodiment of the present invention,
illustrated schematically in FIG. 1b, is substantially similar to
the above-described first embodiment, except that information for
producing a three-dimensional model of object 16 is obtained from
an additional set of photographs in which object 16 is illuminated
by a source of structured light. In this embodiment, a structured
light source 20, such as a shaped laser beam, discussed more fully
below, illuminates object 16 with structured light, preferably in
the form of a vertical stripe of light, in a manner that permits a
three-dimensional model of object 16 to be extracted from an
additional set of photographs of object 16 taken by camera 12 while
object 16 is illuminated with structured light and rotated between
successive photographings in a manner as described above for the
reflectivity photographs. For example, as seen in FIGS. 5a and 5b,
which are examples of such structured-light photographs, a narrow
vertical stripe of light projected onto object 16 from a
structured-light source 20 located off optical axis 52 of camera 12
will produce narrow bright regions 30 (FIGS. 5a and 5b) in
photographs taken by camera 12. Triangulation of points of regions
30 provides information for constructing a three-dimensional model
of object 16. A three-dimensional model constructed in this manner
can reveal recesses in the surface of object 16. The high-contrast
images obtained with structured lighting ease the computational
burden of determining the three-dimensional model. Because each
structured-light photograph according to this embodiment only
provides information about one side of object 16, a substantially
full rotation of object 16 is required to produce a complete
three-dimensional model of the surface of object 16, rather than a
half rotation, which is sufficient for the above-described first
embodiment, wherein each reflectivity photograph provides
information about two sides of object 16.
[0086] Alternatively, in this second embodiment, object 16 can be
rotated a single time, with lamp 18 and structured light source 20
illuminated by turns such that camera 12 produces an interleaved
set of photographs including both the information for creating the
three-dimensional model and the reflectivity data.
[0087] Returning now to structured light source 20, FIG. 7a
illustrates schematically an elevation view, and FIG. 7b
illustrates schematically a plan view, of a system for structured
lighting of object 16. For simplicity, camera 12 is not shown in
FIG. 7a. Structured-light source 20 is operative to illuminate
object 16 with structured light. Preferably, structured-light
source 20 includes a laser 40, operative to produce a beam of light
44, and an optical system 42 operative to shape beam 44 into a
structured beam 46. Preferably, structured beam 46 has a very
narrow cross-section, preferably no greater than 20 .mu.m, in the
neighborhood of object 16, in a first dimension normal to a
direction of propagation of structured beam 46, and a rather wide
cross section, preferably at least spanning object 16 in the
neighborhood of object 16, in a second dimension normal to both the
first dimension and a direction of propagation of structured beam
46. Thus, structured beam 46 has a substantially linear
cross-section. Preferably, the second dimension is substantially
parallel to axis of rotation 28. When illuminated only by such a
structured beam 46, object 16 will appear to be dark except for a
bright stripe 30. Because structured beam 46 propagates in a
direction that is offset from optical axis 52 of camera 12, bright
stripe 30 appears to camera 12 not as a straight line segment, but
rather as a shape that is a function of the three-dimensional shape
of object 16. Such a structured beam 46 can be produced by a
variety of systems and methods well-know to those skilled in the
art, including, but not limited to, lenses, curved mirrors,
oscillating mirrors, rotating mirrors, and diffraction slits.
[0088] A third, alternative, embodiment of the present invention,
illustrated schematically in FIG. 1c, is substantially similar to
the above-described first embodiment, except that information for
producing a three-dimensional model of object 16 is obtained from
an additional set of photographs in which object 16 is illuminated
from behind so as to produce a set of silhouette photographs. FIGS.
6a and 6b show examples of such silhouette photographs. In this
embodiment a light source 22 is operative, preferably via a
condensing lens 14, to illuminate object 16 from behind such that
camera 12 views object 16 in silhouette. Object 16 is rotated
between successive photographings in a manner as described above
for the reflectivity photographs. The silhouette photographs thus
produced are then used to create a three-dimensional model of
object 16.
[0089] In a manner similar to the above-described first embodiment,
only a half-rotation of object 16 is necessary to provide
silhouette photographs including information about boundaries of
object 16 necessary to construct a three-dimensional model of
object 16.
[0090] In a manner similar to the above-described second (i.e.,
structured-light) embodiment, the high-contrast nature of the
silhouette photographs eases the computational burden of producing
a three-dimensional model.
[0091] Alternatively, in this third embodiment, object 16 can be
rotated a single time, with lamp 18 and light source 22 illuminated
by turns such that camera 12 produces an interleaved set of
photographs including both the information for creating the
three-dimensional model and the reflectivity data. In a manner
similar to that described above for the first embodiment,
silhouette photographs from only a half-rotation of object 16 are
necessary to construct a three-dimensional model of the surface of
object 16, although it is desirable to use reflectivity photographs
corresponding to a substantially full rotation of object 16 to
provide reflectivity information about the surface of object 16,
because, although rotation of object 16 by a half-rotation about
axis 28 does not present new information about the boundaries of
object 16 to camera 12, such rotation does present new reflectivity
information about the surface of object 16 to camera 12.
[0092] Because, in the above-described embodiments, object 16 is
rotated through a small angle between the taking of one
reflectivity photograph and the next, a point on object 16 is
generally visible in more than one reflectivity photograph. Thus,
there are many ways to make use of the reflectivity information
corresponding to any particular point on object 16. In general, a
reflectivity value associated with any particular point on a
surface of the three-dimensional model of object 16 is a function
of the various representations, as determined by formulae 1 and 2,
corresponding to that point in the set of reflectivity photographs
of object 16. Preferably, that function is a weighted average of
the various points. The weightings for such a weighted average can
be selected as desired. For example, equal weighting of
corresponding points in several reflectivity photographs can
compensate for changes in brightness related to changes in the
orientation of a surface relative to lamp 18 and camera 12 as
object 16 is rotated about axis 28. Alternatively, in a degenerate
form of weighted average, the reflectivity information contained in
only a single reflectivity photograph corresponding to a particular
point on a surface of object 16 is used for that point, allowing
for faster and simpler computation. Preferably, this single
reflectivity photograph is the reflectivity photograph wherein the
absolute value of the X' coordinate of the point, as determined by
formula 1, is minimized. All selections and weightings of
reflectivity information are within the scope of the present
invention.
[0093] FIG. 8a illustrates schematically an elevation view of a
system according to the present invention in which optical axis 52
of camera 12 is substantially perpendicular to axis 28. It is
apparent from FIG. 8a that photographs taken by camera 12 of object
16 in such a system do not include a portion of object 16 where
object 16 makes contact with dop 24, and that a portion of object
16 opposite dop 24 will also not be adequately represented in the
photographs. These portions can be made viewable according to the
present invention by performing a second scan of object 16, but
with a different portion of object 16 being in contact with dop
24.
[0094] Information from two scans of object 16, with different
portions of object 16 being in contact with dop 24 during each
respective scan, as described above, can be merged into a single
model of object 16, thus allowing a user to view a single model of
the complete surface of object 16, without any region being missing
because of the need to support object 16 on dop 24. This merging
can be performed using software operative to recognize pairs of
corresponding features in the respective models of object 16
produced during the two scans and to merge the models
accordingly.
[0095] Selecting an optical axis 52 for camera 12 that is slightly
displaced from being perpendicular to axis of rotation 28 of dop
24, as shown schematically in FIG. 8b, can make the portion of
object 16 opposite dop 24 visible, at the expense of a slightly
larger region of object 16 at the contact with dop 24 not being
included in the photographs. Thus, only a single region of object
16 is not visible, rather than two regions. In this variation, the
region of object 16 where dop 24 is contacted can also be made
visible in a second scan of object 16 with a different portion of
object 16 being in contact with dop 24. The two models of object 16
thus made using two scans of object 16 can be combined into a
single model, as described above.
[0096] It can be desirable to obtain information for a
three-dimensional model of object 16 from more than one source,
thus improving the quality of the model obtained. For example, the
structured-light model is capable of revealing recesses in the
surface of object 16, but can sometimes include undesired artifacts
in the form of spurious protrusions from the surface. On the other
hand, the silhouette model does not include undesired artifacts,
but does not reveal recesses in the surface of object 16.
Combination of these two models can produce a model that reveals
recesses in the surface of object 16 without undesired artifacts.
Alternatively, a three-dimensional model based on reflectivity
photographs, of object 16, can be combined with the
structured-light model to suppress artifacts. The use of
combinations of models to produce a three-dimensional model of
object 16 is within the scope of the present invention.
[0097] The present invention thus provides a mechanism for viewing
an image of a three-dimensional object, such as a precious stone,
from any desired angle. The image not only shows the geometry of
the surface of the object, but also shows the coloration of the
surface of the object.
[0098] Although particular examples of mechanisms for the obtaining
of a three-dimensional finite-element model of an object have been
presented herein, the present invention can make use of a
three-dimensional finite-element model obtained by any mechanism,
and the use of three-dimensional finite-element models obtained by
any mechanism is within the scope of the present invention.
[0099] A system according to the present invention can be
implemented as illustrated schematically, by way of example only,
in FIG. 9. In FIG. 9, for the sake of simplicity, several system
components illustrated in more detail in FIGS. 1a-c, etc., such as
dop 24, camera 12, light source 18, etc., are represented as
"peripheral devices" 66. Computer 10 executes machine executable
instructions 62 stored in machine readable storage medium 60.
Machine readable instructions 62 are selected, in accordance with
that which is taught in the present invention, such that execution
of machine readable instructions 62 by computer 10 is operative to
manipulate display 32 and peripheral devices 66 in accordance with
user commands supplied via user interface 64.
[0100] Many alterations and modifications of the system illustrated
in FIG. 9 may be made within the scope of the present invention. It
is to be understood that the example of FIG. 9 is presented herein
by way of illustration only, and is in no way intended to be
considered limiting.
[0101] While the invention has been described with respect to a
limited number of embodiments, it will be appreciated that many
variations, modifications and other applications of the invention
may be made.
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